Programming in Logic: Prolog

Programming in Logic: Prolog Introduction Reading: Read Chapter 1 of Bratko CS 360 - Lecture 1

Declarative Programming • Declarative programming describes what to compute rather than how to compute it. • E.g., blueprints for a house are declarative, they describe what to build not how to build it. • Describing “what” is often much easier than describing “how” (but not always). • Algorithm = Logic + Control (R. Kowalski, 1979) • Logic expressions are declarative. CS 360 - Lecture 1

Advantages of Declarative Style of Programming • Simply encode your knowledge without worrying how the knowledge will be used. • The underlying inference engine uses that knowledge to answer the user’s queries. • Knowledge can be used in many ways: • Is Mary Peter’s sister? • Who is Peter’s sister? • Who is whose sister? CS 360 - Lecture 1

Knowledge Bases • A Knowledge Base has: • Knowledge in the form of: • Facts (e.g., Socrates is a man) • Rules (e.g., All men are mortals) • An inference engine • A Knowledge Base uses its facts, rules, and inference engine to answer questions. • Is Socrates mortal? • yes CS 360 - Lecture 1

Logic Programming & Knowledge Bases • Logic programming languages are one way to implement knowledge bases. • Encode your knowledge base and your queries then the underlying inference engine will attempt to answer your queries. • The inference engine answers your queries by building constructive proofs that your queries are entailed by the knowledge base. CS 360 - Lecture 1

Simple Example: Families • Define the relevant relationships: • mother, father, brother, sister, aunt, uncle, cousin, ancestor, descendant • Store the basic facts: • parents, siblings, and gender • Ask your queries: • Who is whose sister? CS 360 - Lecture 1

Some Rules • motherOf(M,O) :- parentOf(M,O), female(M). • sisterOf(S,P) :- siblingOf(S,P), female(S). • auntOf(A,N) :- sisterOf(A,X), parentOf(X,N). • grandmotherOf(G,P) :- motherOf(G,X), parentOf(P). • ancestor(A,P) :- parentOf(A,P). • ancestor(A,P) :- parentOf(A,X), ancestor(X,P). • ... CS 360 - Lecture 1

Some Facts • male(john). • female(mary). • male(peter). • parentOf(john, mary). • siblingOf(mary, peter). • parentOf(ann, john). • parentOf(mark, ann). • ... CS 360 - Lecture 1

Some Queries • ?- sisterOf(mary, peter). • ?- sisterOf(mary, Who). • ?- sisterOf(Sis, peter). • ?- sisterOf(Sister, Sibling). • ?- ancestorOf(A,P). CS 360 - Lecture 1

Their Answers • ?- sisterOf(mary, peter). • yes • ?- sisterOf(mary, Who). • Who = peter ? ; • no • ?- sisterOf(Sis, peter). • Sis = mary ?; • no CS 360 - Lecture 1

More Answers • ?- sisterOf(Sister, Sibling). • Sibling = peter, • Sister = mary ?; • no CS 360 - Lecture 1

Last Answer • ?- ancestorOf(A,P). • A = john, • P = mary ?; • A = ann, • P = john ?; • A = mark, • P = ann ?; • A = ann, • P = mary ? ; • ... CS 360 - Lecture 1

Running Prolog • Create knowledge base using favorite editor. • Type /usr/local/bin/prolog on cs26. • Load that knowledge base into Prolog: • [‘myKnowledgeBase.pl’]. • Ask queries: • sisterOf(X,Y). • Exit Prolog: • halt. CS 360 - Lecture 1

Prolog Knowledge Base Anatomy • Knowledge Base • Relations • Clauses • Terms CS 360 - Lecture 1

Terms • Terms are things like atoms, numbers, variables, and structures: • tom, 25.3, X, name(mike, barley) • In happy(P) :- paid(P, X), spend(P,Y), X>Y happy(P), :-, paid(P, X), spend(P,Y), X>Y, P, X, and Y are all terms. CS 360 - Lecture 1

Anatomy of a Clause • All clauses terminated by full-stop(“.”). • Clauses have the form: • head :- body . CS 360 - Lecture 1

Head of a Clause • The head may be the relation name with arguments or may be missing, Examples: • likes(X,Z) :- likes(X,Y), likes(Y,Z). • likes(mike,X) :- true. • :- write(***). • likes(mike,X) :- true. likes(mike,X) . • Clauses with missing bodies are called facts. • Facts with variables are called universal facts. CS 360 - Lecture 1

Body of a Clause • Body is an expression composed of terms. • When the clause head is missing then the body is executed at load-time. CS 360 - Lecture 1

Anatomy of a Relation • A relation is identified by its name and its arity (# of arguments) - name/arity • likes/2 is a different relation from likes/3 • A relation is defined by the clauses whose heads match the relation id, e.g., the clause • ancestor(A, P) :- parentOf(A, P). is part of the definition of ancestor/2 CS 360 - Lecture 1

Anatomy of a Query • Queries are input by the user (rather than part of the knowledge base). • Queries have clause body syntax & semantics, notably variables are existentially quantified. • When query has variables, & Prolog succeeds in proving it follows from KB, Prolog displays variable bindings used in proof. CS 360 - Lecture 1

Quick Quiz • What do you ignore (at least initially) in declarative-style programming? • What are the two main components of a knowledge-based system? • What is the type of knowledge encoded in a Prolog knowledge base? CS 360 - Lecture 1

Quick Quiz cont’d • By what two things are relations identified? • In a Prolog knowledge base, what constitutes the definition of a relation? • What forms can a clause take? • What are the two parts of a clause? • What terminates a clause? • Give examples of different types of terms. CS 360 - Lecture 1

Summary • Declarative programming focuses on specifying what you want, not on how to get it. • Knowledge based systems provide an underlying inference engine, the user provides (in declarative form) the knowledge and the queries. • Prolog can be viewed as a type of knowledge based programming system. CS 360 - Lecture 1

Summary cont’d • Prolog knowledge base = relation collection. • Relation identified by name/arity. • Relation defined by clauses whose heads agree with that id (i.e., name & number of arguments) CS 360 - Lecture 1

Summary cont’d • Clauses have following forms: • head :- body . • head . • :- body . • Queries are entered by the user (i.e., not in knowledge base) and have form of clause body. CS 360 - Lecture 1

Programming in Logic: Prolog